Research & Publications
Mathematical Foundations and Theoretical Work
Clinical Research
Pediatric Walking Speed Normal Reference Values in a Local Population
Pediatric Physical Therapy, 2023;35(3):326-331
doi:10.1097/PEP.0000000000001015
My Role: Statistical analysis and methodology (third author)
Methods: R (version 4.1.3), IBM SPSS
Analysis: 13×2×2 factorial ANOVA with Type III sum of squares, 1,593 participants ages 5-17
Impact: Normative reference values for assessing children with disabilities in rural Alaska school district
Interdisciplinary collaboration applying statistical methods to clinical physical therapy research. Large dataset management (1,593 children) and rigorous factorial analysis examining main effects and two-way interactions for age, sex, and footwear.
Pure Mathematics
Spectral Conditions for Composition Operators on Algebras of Functions
Communications in Mathematics and Applications, 2012;3(1)
Research on spectral preserving maps between function algebras. Extends results on composition operators in commutative Banach algebras. Co-authored with dissertation advisor.
Ph.D. Dissertation (2013)
Peripherally-Multiplicative Spectral Preservers Between Function Algebras
University of Montana, Missoula, MT
Advisor: Dr. Thomas Tonev
Field: Commutative Banach Algebras, Functional Analysis
(Coming soon: Mobile-friendly version with beautifully rendered mathematics)
Established general sufficient conditions for maps between function algebras to be composition or weighted composition operators. Defined and characterized weakly peripherally-multiplicative and almost peripherally-multiplicative maps. Extended theory to function algebras without unit on locally compact Hausdorff spaces.
Theoretical Computer Science Exploration
Active learning through collaborative study, 2023–Present
Student Collaboration
Lukas Renner (MIT early admission candidate)
Format: Collaborative exploration, 2-3 meetings/week, 1+ year
"Much of the time, we were learning together"
Topics Explored
Theoretical Foundations
- Lambda calculus and mathematical representation
- Formal languages and automata theory
- Propositional logic and proof systems
Abstract Algebra
- Field and ring theory
- Galois fields (cryptographic applications)
- Quotient objects and representatives
Applied Cryptography
- Elliptic curve cryptography
- Mathematical representations in finite fields
- Implementation considerations (student's Rust work)
Computational Mathematics
- Computational linear algebra
- Matrix operations and performance
- Dimension and complexity constraints
Theory Informing Practice
These explorations directly inform implementation work:
- Abstract algebra → cryptographic implementations
- Lambda calculus → functional paradigms in distributed systems
- Category theory → composable system design
- Formal methods → policy verification (MAAT Framework)
Education
Ph.D. Mathematical Sciences
University of Montana, 2008–2013
Advisor: Dr. Thomas Tonev
Commutative Banach Algebras, Functional Analysis
M.S. Coursework — Mathematical Modeling
Humboldt State University, 2004–2005
Environmental Systems
B.A. Mathematics
Humboldt State University, 2002–2004
Continuing Education
- Machine Learning (completed with certificate) — Andrew Ng, Stanford University/Coursera. Supervised learning, neural networks, unsupervised learning, ML system design.
- OLC Online Teaching Certificate Program (2019) — Foundations + electives (retention strategies, gamification, accessibility). Applied to Applied Calculus online course.
- AARMS Graduate Summer School (2010) — Atlantic Association of Research and Mathematical Sciences. University of New Brunswick, Canada. Courses: Topological Combinatorics, Algebraic Topology.
- Function Spaces and Lineability IX (2015) — Spring School on Analysis, Charles University, Czech Republic.